Data structure: \(O = (W, A, Z, Y)\)
Underlying data generating process, \(P_{U,X}\)
## W A Z Y
## Min. :-3.777088 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:-0.646166 1st Qu.:0.584 1st Qu.:0.0000 1st Qu.:0.0000
## Median : 0.003599 Median :1.975 Median :0.0000 Median :0.0000
## Mean : 0.007583 Mean :2.100 Mean :0.4858 Mean :0.2532
## 3rd Qu.: 0.673761 3rd Qu.:3.386 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. : 3.725200 Max. :5.000 Max. :1.0000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.464 2.843 2.753 4.200 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.8976 2.2133 2.2891 3.6245 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.3664 1.7641 1.8995 3.0844 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.152 1.499 2.536 5.000
## CV selected lambda (from one sample): 0.0041344192189172
## The average of CV selected lambdas (from 1000 sample): 0.00502291469916564
## z=1:
## z=0:
## Undersmoothed lambda: 0.000965685169251822
## which is 0.233572146909012 * lambda_CV
## CV selected lambda (from one sample): 0.00179663135270864
## The average of CV selected lambdas (from 1000 sample): 0.00167069905743632
## z=1:
## z=0:
## Undersmoothed lambda: 0.000291732819942546
## which is 0.162377673918872 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000270475505996292
## which is 0.155768441258726 * the average of 1000 lambda_CV
## z=1:
## z=0:
## CV selected lambda (from one sample): 0.000284242765357572
## The average of CV selected lambdas (from 1000 sample): 0.00072537755501008
## z=1:
## z=0:
## Undersmoothed lambda: 4.61546787671019e-05
## which is 0.162377673918872 * lambda_CV